Kirchhoff's Voltage Law

Q. A capacitor of capacitance $C_1=1.0\mu \text{F}$ withstand a maximum voltage $E_1=6.0\text{kV}$ while a capacitor of capacitance $C_2=2.0\mu \text{F}$ can withstand the maximum voltage $E_2=4.0\text{kV}$. For what voltage will the system of these two capacitors with stand , if they both are connected in series ?

1. $9\text{kV}$
2. $10\text{kV}$
3. $11\text{kV}$
4. $12\text{kV}$

Q. What is the electrostatic pressure on the plate of a PPC of capacitance $2\mu \text{F}$ separated by $2\text{mm}$ and $20\text{V}$ potential difference is applied across the capacitor?

1. $2.425\times {10}^{-5}\text{Pa}$
2. $1.425\times {10}^{-5}\text{Pa}$
3. $4.425\times {10}^{-4}\text{Pa}$
4. $7.425\times {10}^{-4}\text{Pa}$

Q. In the circuit shown in figure, $AC$ source gives a voltage $V=20\cos 2000t$. Neglecting source resistance, ammeter readings will be

1. $2.5\text{A}$
2. $1.4\text{A}$
3. $1.6\text{A}$
4. $2.0\text{A}$

Q.

In the circuit shown, the charge on $5\mathrm{\mu F}$ the capacitor is:

1. $5.45\mathrm{\mu C}$

2. $18.00\mathrm{\mu C}$

3. $10.90\mathrm{\mu C}$

4. $16.36\mathrm{\mu C}$

Q. Two identical batteries, each of emf $2\text{V}$ and internal resistance $r=1\Omega$ are connected as shown. The maximum power that can be developed across $R$ using these batteries is

1. $3.2\text{W}$
2. $8.2\text{W}$
3. $2\text{W}$
4. $4\text{W}$

Q. If the two dielectrics of dielectric constant $K_1$ & $K_2$ with thickness $t_1$ & $t_2$ respectively, were to be replaced by a single dielectric completely filling the space between the two plates, then its equivalent dielectric constant will be

1. $\frac{K_1{K}_2(t_1+t_2)}{K_1{t}_1+K_2{t}_2}$
2. $\frac{K_1{K}_2(t_1+t_2)}{K_1{t}_2+K_2{t}_1}$
3. $\frac{2K_1{K}_2(t_1+t_2)}{K_1{t}_2+K_2{t}_1}$
4. $\frac{K_1{K}_2(t_1+t_2)}{2(K_1{t}_1+K_2{t}_1)}$

Q. $\text{Statement I}$
To get a steady $dc$ output from the pulsating voltage received from a full wave rectifier, we can connect a capacitor across the output parallel to the load $R_L$.
$\text{Statement II}$
To get a steady dc output from the pulsating.voltage received from a full wave rectifier, we can connect an inductor in series with $R_L$.

In the light of the above statements, choose the most appropriate answer from the options given below:

1. Both $\text{Statement I}$ and $\text{Statement II}$ are true
2. $\text{Statement I}$ is false but $\text{Statement II}$ is true.
3. $\text{Statement I}$ is true but $\text{Statement II}$ is false
4. Both $\text{Statement I}$ and $\text{Statement II}$ are false

Q. In the circuit shown, what is the potential difference $V_{PQ}$ between points $P$ and $Q$?

1. $+3\text{V}$
2. $+2\text{V}$
3. $-2\text{V}$
4. None

Q. In a series $\text{LCR}$ circuit, voltage drop across resistance is $8\text{V}$ , across inductor is $6\text{V}$ and across capacitor is $12\text{V}$. Then,

1. Voltage of the source will be leading in the circuit.
2. Voltage drop across each element will be less than the applied voltage.
3. Power factor of the circuit will be $\frac{3}{4}$.
4. None of the above.

Q. In he given circuit, a charge of $+80\mu C$ is given to the upper plate of the $4\mu F$ capacitor. Then in the steady state, the charge on the upper plate of the $3\mu F$ capacitor is

Diagram

1. $+48\mu C$
2. $+80\mu C$
3. $+40\mu C$
4. $+32\mu C$

Q. You are given many resistors, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of $50Hz$ frequency (the next three circuits) in different ways as shown in Column II. When a current $I$ (steady state for DC or rms for AC) flows through the circuit, the corresponding voltages $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column I. Match the two columns.
Column I Column II

i.	$I\ne 0,V_1$ is proportional to $I$	a.
ii.	$I\ne 0,V_2>V_1$	b.
iii.	$V_1=0,V_2=V$	c.
iv.	$I\ne 0,V_2$ is proportional to $I$	d.
		e.

1. i - c, d, e ; ii - b, c, d, e ; iii - a, b ; iv - b, c, d, e
2. i - c, d, e ; ii - b, c, e ; iii - a, b ; iv - b, c, d, e
3. i - c, e ; ii - b, c, d, e ; iii - a, b ; iv - b, c, e
4. i - c, d ; ii - b, d, e ; iii - a, b ; iv - b, d, e

Q. In the circuit shown below, if the resistance $5\Omega$ develops a heat 42J per second, then heat developed in $2\Omega$ must be about:

1. 30 J/s
2. 20 J/s
3. 25 J/s
4. 35 J/s

Q. The capacitor $C_1$ in the figure initially carries a charge $q_0$. When the switch $S_1$ and $S_2$ are closed, capacitor $C_1$ is connected to a resistor $R$ and a second capacitor $C_2$ which initially does not carry any charge. The current $i$, through resistor $R$ as a function of time $t$ is represented as:

1. $i=\frac{q_0}{C_1}{e}^{[\frac{-t(C_1+C_2)}{R}]}$
2. $i=\frac{q_0}{C_{1}R}{e}^{[\frac{-t(C_1+C_2)}{C_1{C}_{2}R}]}$
3. $i=\frac{2q_0}{C_{1}R}{e}^{[\frac{-t}{C_{2}R}]}$
4. $i=\frac{2q_0}{C_{2}R}{e}^{[\frac{-t}{C_{1}R}]}$

Q. A resistance $R$, an inductance $L$ and a capacitor $C$ are all connected in series with an $AC$ supply. The resistance is of $16\Omega$ and for a given frequency, the inductive reactance of $L$ is $24\Omega$ and capacitance reactance of $C$ is $12\Omega$. If the current in the circuit is $5\text{A}$, find the potential difference across $R,L\text{and}C$ in $\left(\text{V}\right)$.

1. $120,120,60$
2. $80,120,60$
3. $80,80,80$
4. $60,80,100$

Q. The parallel combination of two air filled parallel plate capacitors of capacitance $C$ and $nC$ is connected to a battery of voltage, $V$. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant $K$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is-

1. $V$
2. $\frac{V}{K+n}$
3. $\frac{(n+1)V}{(K+n)}$
4. $\frac{nV}{K+n}$

Q. A cell develops the same power across two resistance $R_1$ and $R_2$ separately. The internal resistance of the cell is-

1. $\sqrt{R_1{R}_2}$
2. $\sqrt{R_1+R_2}$
3. $R_1+R_2$
4. $\sqrt{\frac{R_1}{R_2}}$

Q.

Find the potential difference $V_a-V_b$ in the circuits shown if figure (32-E12).

Figure 32 - E12

Q. Three identical bulbs are connected in series and these together dissipate a power $P$. If now these bulbs are connected in parallel, then the power dissipated will be

1. $\frac{P}{3}$
2. $3P$
3. $9P$
4. $\frac{P}{9}$

Q. In figure, if the potential at point $P$ is $100\text{V}$, what is the potential at point $Q$?

1. $10\text{V}$
2. $-20\text{V}$
3. $20\text{V}$
4. $-10\text{V}$

Q. In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance $C\mu \text{F}$ across a $200\text{V},50\text{Hz}$ supply. The power consumed by the lamp is $500\text{W}$ while the voltage drop across it is $100\text{V}$. Assume that there is no inductive load in the circuit. Take $rms$ values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is $\varphi$.

Assume, $\pi \sqrt{3}\approx 5$.

The value of $C$ is -

Q. If the charge on left plate of the $5\mu \text{F}$ capacitor in the circuit segment shown in the figure is $-20\mu \text{C}$, then the charge on the right plate of $3\mu \text{F}$ capacitor is:

1. $+8.58\mu \text{C}$
2. $-8.58\mu \text{C}$
3. $+11.42\mu \text{C}$
4. $-11.42\mu \text{C}$

Q. A parallel plate capacitor is made using three different dielectric materials as shown in figure. Separation between the plates of the capacitor is $d$. The equivalent capacitance between the plates is

1. $\frac{{\epsilon }_{0}KA}{d}$
2. $\frac{2{\epsilon }_{0}KA}{d}$
3. $\frac{3{\epsilon }_{0}KA}{d}$
4. $\frac{5{\epsilon }_{0}KA}{d}$

Q. Find charge on each capacitor in the given circuit?

1. $46\mu \text{C},54\mu \text{C},7\mu \text{C}$
2. $66\mu \text{C},7.5\mu \text{C},58.5\mu \text{C}$
3. $58.5\mu \text{C},7.5\mu \text{C},60\mu \text{C}$
4. $7.5\mu \text{C},36\mu \text{C},55\mu \text{C}$

Q. Both capacitors are initially uncharged and then connected as shown and switch is closed. What is the potential difference across the $3\mu F$ capacitor?

1. $30\text{V}$
2. $10\text{V}$
3. $25\text{V}$
4. None of these

Q. A current of $2\text{mA}$ was passed through an unknown resistor which dissipated a power of $4.4\text{W}$. Dissipated power when an ideal power supply of $11\text{V}$ is connected across it is

1. $11\times {10}^{-5}\text{W}$
2. $11\times {10}^{-3}\text{W}$
3. $11\times {10}^{-4}\text{W}$
4. $11\times {10}^5\text{W}$

Q. Calculate the steady state current in the $2\Omega$ resistor and steady state charge on the capacitor in the circuit?

1. $0.9\text{A};0.36\mu \text{C}$
2. $0.7\text{A};0.27\mu \text{C}$
3. $0.5\text{A};0.20\mu \text{C}$
4. $0.2\text{A};2\mu \text{C}$

Q. A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants $K_1=2,K_2=4,K_3=6$ and $K_4=8$ arranged as shown in the figure. The effective dielectric constant will be

1. $3.8$
2. $4.8$
3. $1.8$
4. $2.8$

Q. In the given circuit, in the steady state condition, the potential drop across the capacitor must be-

1. $V$
2. $\frac{V}{2}$
3. $\frac{V}{3}$
4. $\frac{2V}{3}$

Q. A part of the circuit as shown in the figure. All the capacitors have capacitance of $2\mu F$, then charge on

1. capacitor $C_1$ is zero
2. capacitor $C_2$ is zero
3. capacitor $C_3$ is zero
4. any capacitor cannot be determined

Q. In the given circuit, if the galvanometer shows zero reading, then
x= ___ ohms

1. 30
2. 50
3. 100
4. 20